Precal Blog

Really the only thing that came up in class worth mentioning is that although we have spent the last week on logarithms we spent twice that amount of time on other functions. This means that the test will reflect that by being about two-thirds 7-2, 7-3 and about one-third logarithms. I plan on having each learning target represented.

My only other advice is that you don’t memorize, but you use what you know about the concepts to reason through the problems. Memory can fail you and your problem solving skills are definately more reliable.

Make sure that you can rewrite a “power function with a rational
exponent” as a “radical (square root, cube root, etc.) function”. It
seemed to me that we were relying too much on whether or not the
numerator and denominator are even or odd when trying to determine the domain and range. If you rewrite the function as a radical then it should be clear whether or not negatives are allowed in the domain and also whether or not you will get negatives in your range.

Presentations on 7-3 tomorrow. Don’t forget – the Wiki needs information!

My goal is for the technology we use to enhance the learning that goes
on. If it is a hassle to use, or inconvenient then I don’t think it
will be useful. Please keep me informed on what works, what doesn’t,
and what other kinds of things we could be doing. Keep in mind that
this blog will be mostly static in that it will provide you with a
rundown of the day’s events and provide you with links for further
consideration. The wiki is meant to be dynamic and constantly growing
with new information. The catch is that the wiki needs your
input. Please respect both of these forums and use them responsibly.

Just a side note on power functions from today: I mentioned that your
calculator treats something like “x to the four-thirds power” very
differently than “x to the 1.333…” This has to do with the way the
calculator is programmed – just another reason to always reconcile what you know with what your calculator is telling you.

Oh yeah, before I forget – this blog may be of interest to you.

We discussed 7-2 claims today. Didn’t seem like there were any major issues. We still have an unanswered question hanging out there though: why are we allowed to divide the two equations in systems created for power and exponential functions?

We also talked briefly about e. I’ll look for some specific links on e and add them to our del.icio.us feed.

We talked about rational, negative, and negative rational b-values today. As a prerequisite we had to discuss how to write rational exponents as “roots”. We discovered that the denominator of the exponent told us what root of x we are taking (which in turn tells us something about the domain) and the numerator tells us to what power we take that root (which tells us something about the range).

We also discovered that even powered functions appear in the 1st and 2nd quadrant while odd powered functions appear in the 1st and 3rd quadrant. When the b-value is negative this puts x in the denominator which means the function is undefined for zero. We will do presentations tomorrow on both 7-2 and power functions (7-2a).